

import gc
import threading
import time

import psutil
import torch






class       __magic_name__       :





			def __init__(						self   )  ->					Optional[Any]:




						'''simple docstring'''
						__a     =psutil.Process()
						__a     =False





			def 						__magic_name__       (						self   )  ->					Any:




						'''simple docstring'''
						__a     =-1

						while True:
									__a     =max(self.process.memory_info().rss   ,    self.cpu_memory_peak   )

									# can't sleep or will not catch the peak right (this comment is here on purpose)
									if not self.peak_monitoring:
												break





			def 						__magic_name__       (						self   )  ->					Optional[Any]:




						'''simple docstring'''
						__a     =True
						__a     =threading.Thread(target=self.peak_monitor   )
						__a     =True
						self.thread.start()





			def 						__magic_name__       (						self   )  ->					Union[str, Any]:




						'''simple docstring'''
						__a     =False
						self.thread.join()
						return self.cpu_memory_peak


_lowerCAmelCase   :     str    							=     PeakCPUMemory()






def 			UpperCamelCase_(				):




			"""simple docstring"""






			__a     ={'time': time.time()}

			gc.collect()
			torch.cuda.empty_cache()

			# CPU mem
			__a     =psutil.Process().memory_info().rss
			cpu_peak_tracker.start()

			# GPU mem
			for i in range(torch.cuda.device_count()      ):
						__a     =torch.cuda.memory_allocated(_A      )
			torch.cuda.reset_peak_memory_stats()

			return measures






def 			UpperCamelCase_(				_snake_case  :    Dict      ):




			"""simple docstring"""






			__a     ={'time': time.time() - start_measures['time']}

			gc.collect()
			torch.cuda.empty_cache()

			# CPU mem
			__a     =(psutil.Process().memory_info().rss - start_measures['cpu']) / 2**20
			__a     =(cpu_peak_tracker.stop() - start_measures['cpu']) / 2**20

			# GPU mem
			for i in range(torch.cuda.device_count()      ):
						__a     =(torch.cuda.memory_allocated(_A      ) - start_measures[str(_A      )]) / 2**20
						__a     =(torch.cuda.max_memory_allocated(_A      ) - start_measures[str(_A      )]) / 2**20

			return measures






def 			UpperCamelCase_(				_snake_case  :    Optional[int]			,	_snake_case  :    int      ):




			"""simple docstring"""






			print(F'{description}:'      )
			print(F'- Time: {measures["time"]:.2f}s'      )
			for i in range(torch.cuda.device_count()      ):
						print(F'- GPU {i} allocated: {measures[str(_A      )]:.2f}MiB'      )
						__a     =measures[F'{i}-peak']
						print(F'- GPU {i} peak: {peak:.2f}MiB'      )
			print(F'- CPU RAM allocated: {measures["cpu"]:.2f}MiB'      )
			print(F'- CPU RAM peak: {measures["cpu-peak"]:.2f}MiB'      )










def 							UpperCamelCase_(					_A :list[list]	)->		list[list]:
			UpperCamelCase__       =							current_set.copy()
			for row_index, row in enumerate(_A	):
						UpperCamelCase__       =							row[0]
						for column_index, column in enumerate(_A	):
									if magnitude == 0:
												UpperCamelCase__       =							column
												continue
									UpperCamelCase__       =							column / magnitude
    # Subtract to cancel term
			UpperCamelCase__       =							current_set[0]
			UpperCamelCase__       =							[first_row]
			UpperCamelCase__       =							current_set[1::]
			for row in current_set:
						UpperCamelCase__       =							[]
						# If first term is 0, it is already in form we want, so we preserve it
						if row[0] == 0:
									final_set.append(_A	)
									continue
						for column_index in range(len(_A	)	):
									temp_row.append(first_row[column_index] - row[column_index]	)
						final_set.append(_A	)
			# Create next recursion iteration set
			if len(final_set[0]	) != 3:
						UpperCamelCase__       =							final_set[0]
						UpperCamelCase__       =							[]
						UpperCamelCase__       =							[]
						for row in final_set[1::]:
									current_first_column.append(row[0]	)
									next_iteration.append(row[1::]	)
						UpperCamelCase__       =							simplify(_A	)
						for i in range(len(_A	)	):
									resultant[i].insert(0					,  current_first_column[i]	)
						resultant.insert(0					,  _A	)
						UpperCamelCase__       =							resultant
			return final_set
def 							UpperCamelCase_(					_A :list[list]	)->		list:
			if len(_A	) == 0:
						raise IndexError("solve_simultaneous() requires n lists of length n+1"	)
			UpperCamelCase__       =							len(_A	) + 1
			if any(len(_A	) != _length for item in equations	):
						raise IndexError("solve_simultaneous() requires n lists of length n+1"	)
			for row in equations:
						if any(not isinstance(_A					,  (int, float)	) for column in row	):
									raise ValueError("solve_simultaneous() requires lists of integers"	)
			if len(_A	) == 1:
						return [equations[0][-1] / equations[0][0]]
			UpperCamelCase__       =							equations.copy()
			if any(0 in row for row in data_set	):
						UpperCamelCase__       =							data_set.copy()
						UpperCamelCase__       =							[]
						for row_index, row in enumerate(_A	):
									if 0 not in row:
												UpperCamelCase__       =							data_set.pop(_A	)
												break
						if not full_row:
									raise ValueError("solve_simultaneous() requires at least 1 full equation"	)
						data_set.insert(0					,  _A	)
			UpperCamelCase__       =							data_set.copy()
			UpperCamelCase__       =							simplify(_A	)
			UpperCamelCase__       =							simplified[::-1]
			UpperCamelCase__       =							[]
			for row in simplified:
						UpperCamelCase__       =							row[-1]
						if not solutions:
									if row[-2] == 0:
												solutions.append(0	)
												continue
									solutions.append(current_solution / row[-2]	)
									continue
						UpperCamelCase__       =							row.copy()[: len(_A	) - 1 :]
						while temp_row[0] == 0:
									temp_row.pop(0	)
						if len(_A	) == 0:
									solutions.append(0	)
									continue
						UpperCamelCase__       =							temp_row[1::]
						UpperCamelCase__       =							temp_row[::-1]
						for column_index, column in enumerate(_A	):
									current_solution -= column * solutions[column_index]
						solutions.append(_A	)
			UpperCamelCase__       =							[]
			for item in solutions:
						final.append(float(round(_A					,  5	)	)	)
			return final[::-1]


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						__UpperCamelCase     		=							[
						    [2, 1, 1, 1, 1, 4],
						    [1, 2, 1, 1, 1, 5],
						    [1, 1, 2, 1, 1, 6],
						    [1, 1, 1, 2, 1, 7],
						    [1, 1, 1, 1, 2, 8],
						]
						print(solve_simultaneous(eq))
						print(solve_simultaneous([[4, 2]]))


